A Fast Algorithm for Exact Maximum Likelihood Estimation of Multiple Input Transfer Function Models with Auto-Correlated Errors

Abstract

This paper proposes a fast algorithm for the exact maximum likelihood estimation of parameters of multiple inputs transfer function models. This algorithm is a generalization of that proposed by Mélard (1984) which is a combination of an improved version of an algorithm of Pearlman (1980) which uses an algorithm of Morf, Sidhu et Kailath (1974) and consists to replace the (matrix) Riccati-type difference equation used in the Kalman filter by a (vector) Chandrasekhar-type difference equation with the quick recursion switching suggested by Gardner, Harvey and Phillips (1980) and an algorithm of Wilson (1979). Simulations and practical examples are used to illustrate the algorithm by comparing it with the method of Poskitt (1989), the generalized least squares method suggested by Sabiti (1993), and the nonlinear least-squares method of Box and Jenkins (1976).